Answer:
Only option A is correct.
Step-by-step explanation:
From the given figure it is noticed that the vertices of hyperbola are (0,8) and (0,-8). It is a vertical hyperbola.
It means a=8.
From the rectangle we can say that the value of b is 6.
[tex]c^2=a^2-b^2[/tex]
[tex]c^2=(8)^2+(6)^2[/tex]
[tex]c^2=100[/tex]
[tex]c=10[/tex]
The focus of a vertical hyperbola are (0,c) and (0,-c). So, the focus of hyperbola are (0,10) and (0,-10).
Therefore option A is correct.
Asymptotes of a vertical hyperbola are
[tex]y=\pm \frac{a}{b}x[/tex]
[tex]y=\pm \frac{8}{6}x[/tex]
[tex]y=\pm \frac{4}{3}x[/tex]
Directrix of a vertical hyperbola are
[tex]y=\pm \frac{a^2}{c}[/tex]
[tex]y=\pm \frac{(10)^2}{6}[/tex]
[tex]y=\pm \frac{50}{3}[/tex]
Only option A is correct.
